A novel type of ER3BP introduced for hierarchical configuration with variable angular momentum of secondary planet

Ershkov, Sergey V.; Abouelmagd, Elbaz I.; Rachinskaya, Alla

doi:10.1007/s00419-021-02027-8

Cited by 21 publications

(17 citation statements)

References 28 publications

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“…According to results of [8], let us present Eqns. ( 2)-( 4) after transforming of their right parts with help of partial derivatives with respect to the proper coordinates as below in a form convinient for further numercial solving (in next Sections).…”

Section: Form Of Analytical Presentation Of Eqns (2)-(3) Convinient F...mentioning

confidence: 99%

“…We should especially remark (see [8]) that for using of the time-dependent eccentricity e(t) in Eqns ( 2)-(3) or equivalently in Eqns. (5) we should first solve Eqn.…”

Section: The Way Of Taking Into Account the Variable Eccentricity E(f...mentioning

confidence: 99%

“…In this work, we will assume that small planetoid m is orbiting near the natural moon m moon of planet in Solar system with variable eccentricity of the moon in its motion around the planet (this kind of motion was considered previously in [8]).…”

Section: Introductionmentioning

confidence: 99%

“…The relative distance  of the positions of primaries are always changing in mutual permanent motion (in the ER3BP) on their elliptical orbits [1] where, a p is the semimajor axis of elliptic orbits of primaries around their common centre of mass (here, scale of distances is chosen so that {a p (0)*(1e(0)} = 1), e is the variable eccentricity, f is the true anomaly. As formulated in [8], angular motion is given by where, G is the Gaussian constant of gravitation law, M is the sum of masses of primaries, the unit of time is chosen so that constant G equals to 1.…”

Section: Introductionmentioning

confidence: 99%

“…According [8][9][10], equations of ER3BP for small planetoid m can be presented in the synodic co-rotating Cartesian coordinate system {x, y, z} in non-dimensional scaled form (we consider here Cauchy problem with given initial conditions):…”

Section: Introductionmentioning

confidence: 99%

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On the Motion of Small Satellite near the Planet in ER3BP

2021

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In the current study, we explore stability of motion of satellite around the natural moons of planets in Solar system using the novel concept of ER3BP with variable eccentricity. This concept was introduced earlier when novel type of ER3BP (Sunplanet-satellite) was investigated with variable spin state of secondary planet correlated implicitly to the motion of satellite (in the synodic co-rotating Cartesian coordinate system) for its trapped orbit near the secondary planet (which is involved in kepler duet "Sun-planet"). But it is of real interest to explore another kind of aforedescribed problem, ER3BP (planet-moon-satellite) with respect to investigation of motion of satellite m around the natural moon m moon of planet in Solar system with variable eccentricity of the moon in its motion around the planet. So, we consider here two primaries, M planet and m moon, the last is orbiting around their common barycenter on quasi-elliptic orbit with slow-changing, not constant eccentricity (on a large-time scale) due to tidal phenomena. Our aim is to investigate motion of small dot satellite around the natural moon of planet on quasistable elliptic orbit. Both novel theoretical and numerical findings (for various cases of trio "planet-moon-satellite") are presented in the current research.

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Section: Form Of Analytical Presentation Of Eqns (2)-(3) Convinient F...mentioning

confidence: 99%

“…We should especially remark (see [8]) that for using of the time-dependent eccentricity e(t) in Eqns ( 2)-(3) or equivalently in Eqns. (5) we should first solve Eqn.…”

Section: The Way Of Taking Into Account the Variable Eccentricity E(f...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the Motion of Small Satellite near the Planet in ER3BP

2021

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Single Variable Regression Model with Error Analysis for Evolution of Periodic Orbit in Formation Satellite

Doshi

Pathak

Abouelmagd

2023

Advances in Intelligent Systems and Computing

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Revisiting the dynamics of finite-sized satellite near the planet in ER3BP

2022

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A novel approach for solving equations of motion of finite-sized satellite supposed to be moving in a proximity and around the planet in the elliptic restricted three-body problem, ER3BP is presented in this semi-analytical investigation. We consider two primaries, M Sun and m planet (the last is secondary in that binary system), both are orbiting around their barycenter on elliptic orbits. Satellite is considered to be the solid ellipsoid having nearly spherical form, with its gravitational potential to be given by a formula of MacCullagh type.Our aim is to revisit previously presented in work [Ashenberg, 1996] approach and to investigate the updated type of the satellite dynamics correlated implicitly to a kind of trapped motion (in the synodic co-rotating Cartesian coordinate system) in so way that satellite will always to be located near the secondary planet, m planet, moving on quasi-stable elliptic orbit.

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A novel type of ER3BP introduced for hierarchical configuration with variable angular momentum of secondary planet

Cited by 21 publications

References 28 publications

On the Motion of Small Satellite near the Planet in ER3BP

On the Motion of Small Satellite near the Planet in ER3BP

Single Variable Regression Model with Error Analysis for Evolution of Periodic Orbit in Formation Satellite

Revisiting the dynamics of finite-sized satellite near the planet in ER3BP

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